BEC–BCS crossover in a (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>i</mml:mi><mml:mi>p</mml:mi></mml:math>)-wave pairing Hamiltonian coupled to bosonic molecular pairs

Dunning, Clare; Isaac, Phillip S.; Links, Jon; Zhao, Shengmei

doi:10.1016/j.nuclphysb.2011.03.001

Cited by 12 publications

(25 citation statements)

References 45 publications

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“…It is important to note that in this case there is no signature of any quantum phase transition, no matter how weak the environment coupling is, which is in stark contrast to the closed system. A similar scenario was considered in [22] where the environment was modelled by a single bosonic degree of freedom in such a way that integrability was preserved. There too, arbitrarily small coupling to the environment was found to annihilate the existence of any quantum phase transition.…”

Section: Resultsmentioning

confidence: 99%

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

2018

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Using the exact Bethe Ansatz solution, we investigate methods for calculating the ground-state energy for the p + ip-pairing Hamiltonian. We first consider the Hamiltonian isolated from its environment (closed model) through two forms of Bethe Ansatz solutions, which generally have complex-valued Bethe roots. A continuum limit approximation, leading to an integral equation, is applied to compute the ground-state energy. We discuss the evolution of the root distribution curve with respect to a range of parameters, and the limitations of this method. We then consider an alternative approach that transforms the Bethe Ansatz equations to an equivalent form, but in terms of the real-valued conserved operator eigenvalues. An integral equation is established for the transformed solution. This equation is shown to admit an exact solution associated with the ground state. Next we discuss results for a recently derived Bethe Ansatz solution of the open model. With the aforementioned alternative approach based on real-valued roots, combined with mean-field analysis, we are able to establish an integral equation with an exact solution that corresponds to the ground-state for this case.

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Section: Resultsmentioning

confidence: 99%

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

2018

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“…It is anticipated that this exact result will allow for a detailed analysis of the model in future studies. There are two examples in the literature [32,33] of related pairing models interacting with a single bosonic degree of freedom, where the boson-fermion interaction has the form…”

Section: Resultsmentioning

confidence: 99%

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Lukyanenko¹,

Isaac²,

Links³

2016

J. Phys. A: Math. Theor.

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We consider a generalisation of the p + ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation of particle number, present in the p + ip Hamiltonian, is broken. Nonetheless the generalised model is integrable. We establish integrability using the Boundary Quantum Inverse Scattering Method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe Ansatz Equations, the roots of which parametrise the exact solution for the energy spectrum.

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“…Indeed, any linear combination of the integrals of motion defines an exactly solvable Hamiltonian. In particular, the Hamiltonian studied by Links et al [15], can be obtained from the linear combination H = 2 i ǫ i R i with 2ǫ i = 1/η i . If ǫ k = |k| 2 /2, with 0 k k cut , then the parameters η k entering in the Richardson's equations (5) are defined in the interval 1/|k cut | 2 = 1/(2ω) η k ∞.…”

Section: Pacs Numbersmentioning

confidence: 99%

Integrable two-channelpx+ipy-wave model of a superfluid

Rombouts

Dukelsky

et al. 2011

Phys. Rev. B

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We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the pwave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact manybody wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition. PACS numbers:In recent years p-wave paired superfluids have attracted a lot of attention, in part due to their exotic properties [1]. Of particular interest is the chiral twodimensional (2D) p x + ip y superfluid of spinless fermions, that supports a topological phase with zero energy Majorana modes [2]. The latter are theorized to serve as a basic element for a topological quantum computer [3]. [7] with the potential to manipulate the system from the weak (BCS) to the strong (BEC) pairing regime. However, these gases revealed to be unstable due to atom-molecule relaxation processes in which the molecule decays to a deep bound state while the atom escapes with excess energy [8]. Other atomic and molecular gases are now in consideration, as well as different mechanisms to suppress relaxation.From a theoretical standpoint, despite great efforts to describe these systems, a complete understanding of the BCS-BEC transition and the corresponding phase diagram is still missing. Recently, by means of an exactly solvable p x + ip y pairing model [9,10] it was shown that the quantum phase transition (QPT) taking place from weak pairing to strong pairing can be understood as the deconfinement of bound Cooper pairs [11]. In this Letter we introduce an exactly solvable two-channel p x + ip y pairing model with a Feshbach resonance. Our model is exactly solvable in arbitrary dimensions, although we will concentrate on its 2D realization. We propose a way to experimentally detect the so-called topological QPT [12] from weak to strong pairing, by measuring a densitydensity correlation function. This together with the analysis of the size of a Cooper pair in terms of the exact solution allows the characterization of the transition as one of a confinement-deconfinement type without Landau order parameter. Moreover, the transition is shown to be third order in the Ehrenfest classification. Another way to theoretically detect that QPT is by analyzing the behavior of the quantum fidelity z of the ground state wavefunction. Interestingly, the second order derivative of ln |z| displays a logarithmic singularity at the transition point confirming its third order character.Consider the 2D two-channel p x + ip y -wave model† is a bosonic creation operator, andOur next goal is to show that this model is a particular realization of a family of exactly-solvable atom-molecule Hamiltonians of physical relevance in th...

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BEC–BCS crossover in a (p+ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs

Cited by 12 publications

References 45 publications

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Integrable two-channelpx+ipy-wave model of a superfluid

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BEC–BCS crossover in a (p+ip)-wave pairing Hamiltonian coupled to bosonic molecular pairs

Cited by 12 publications

References 45 publications

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

An integrable case of thep+ ippairing Hamiltonian interacting with its environment

Integrable two-channelpx+ipy-wave model of a superfluid

Contact Info

Product

Resources

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Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz